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ORTHONORMAL GEOMETRIC SEQUENCES AND THEIR Ζ TRANSFORMS

ORTHONORMAL GEOMETRIC SEQUENCES AND THEIR Ζ TRANSFORMS DEMONSTRATIO MATHEMATICAVol. XVIINo 31984Stanislaw KusORTHONORMAL GEOMETRIC SEQUENCESAND THEIR Ζ TRANSFORMS1. IntrodactionBy me axis of -orfhonormal bases i t i s possible to solve•"Asimply the problem of the best approximation of the elementsof β Hilbert spaoe. On the other hand, in view of the development of the theory of d i s c r e t e dynamioal systems and of thed i g i t a l technique i t seems s u i t a2b l e t o construct an orthonormal base i n the Hilbert space 1 .Possible applications of t h i s bases f o r instance aretapproximation of s o l u t i o n of the system of l i n e a r d i f f e r e n c eequations or i d e n t i f i c a t i o n of disorete-time systems i n ooat r o l theory.In t h i s paper orthonormal bases are constructed whose e l e ments are l i n e a r oomblnätions of geometrio sequences. Thisbases are obtained by the transformation <z and orthonoroaliz a t i o n i n complex http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ORTHONORMAL GEOMETRIC SEQUENCES AND THEIR Ζ TRANSFORMS

Demonstratio Mathematica , Volume 17 (3): 8 – Jul 1, 1984

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References (1)

Publisher
de Gruyter
Copyright
© by Stanislaw Kuś
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1984-0308
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XVIINo 31984Stanislaw KusORTHONORMAL GEOMETRIC SEQUENCESAND THEIR Ζ TRANSFORMS1. IntrodactionBy me axis of -orfhonormal bases i t i s possible to solve•"Asimply the problem of the best approximation of the elementsof β Hilbert spaoe. On the other hand, in view of the development of the theory of d i s c r e t e dynamioal systems and of thed i g i t a l technique i t seems s u i t a2b l e t o construct an orthonormal base i n the Hilbert space 1 .Possible applications of t h i s bases f o r instance aretapproximation of s o l u t i o n of the system of l i n e a r d i f f e r e n c eequations or i d e n t i f i c a t i o n of disorete-time systems i n ooat r o l theory.In t h i s paper orthonormal bases are constructed whose e l e ments are l i n e a r oomblnätions of geometrio sequences. Thisbases are obtained by the transformation <z and orthonoroaliz a t i o n i n complex

Journal

Demonstratio Mathematicade Gruyter

Published: Jul 1, 1984

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